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Q. 103

Expert-verified

The Practice of Statistics for AP Examination

Found in: Page 430

Book edition 6th

Author(s) Daren Starnes, Josh Tabor

Pages 837 pages

ISBN 9781319113339

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Short Answer

Lefties Refer to Exercise 99.
a. Justify why L can be approximated by a Normal distribution.
b. Use a Normal distribution to estimate the probability that 15 or more students in the sample are left-handed.

The $L$ is about regularly distributed.
The resultant probability is $0.1003 .$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Part (a) Step 1: Given information

The number of students $(n) = 100$

Left-handed students as a percentage of total students $(p) = 0.11$

Part (a) Step 2: Calculation

Consider,

$n p = 100 (0.11) = 11 > 10 n (1 - p) = 100 (1 - 0.11) = 89 > 10$

Therefore, the L is about regularly distributed.

Part (b) Step 1: Given information

The number of students $(n) = 100$

Left-handed students as a percentage of total students $(p) = 0.11$

Part (b) Step 2: Calculation

If 15 or more pupils are left-handed, the probability is calculated as"

\begin{array}{rcl} P (X & \geq & 15) = P (Z \geq \frac{15 - 100 (0.11)}{\sqrt{100 (0.11) (1 - 0.11)}}) \\ = & P (Z \geq 1.28) \\ = & 1 - 0.8997 \\ = & 0.1003 \end{array}

Thus, the resultant probability is 0.1003.

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